(226c) Simulating the Particle Size Evolution during Dry Milling Via a Multi-Scale DEM-PBM Approach

Population balance models (PBM) and the discrete element method (DEM) have often been used separately in the simulation of dry milling. While DEM is an excellent method to provide microdynamic information on particulate processes, it does not have the ability to simulate the actual breakage of particles and it is computationally intensive. In fact, due to the ever-increasing number of particles upon breakage, simulating the evolution of the particle size distribution (PSD) in a real milling process via DEM is intractable. On the other hand, PBM can simulate the evolution of PSD efficiently, but it is a process scale model which lacks consideration of particle-scale or microdynamic information. To simulate milling processes with mechanistic, microdynamic information, this study formulates a multi-scale modeling approach which combines the use of DEM and PBM to exploit their advantages while mitigating their limitations. DEM is used to elucidate the effect of milling environment on particle breakage behavior which is input into the PBM to predict the evolution of the PSD.  While DEM and PBM can be used in combination at early milling times to simulate the evolution of the PSD, PBM must be used exclusively at prolonged milling times when particle numbers exceed the computational limit of DEM. As a major novelty, the approach is enhanced by using a non-linear PBM which explicitly accounts for the effect of the milling environment through a so-called effectiveness factor. The effectiveness factor can model the effect of the evolving PSD on breakage behavior and can be used to more accurately predict the PSD within the non-linear PBM framework. This aspect is critical since the sole use of the PBM is required at prolonged milling times when DEM cannot be practically used to elucidate the particle-scale behavior. The DEM-PBM approach detailed in this study is likely the best approach to simulate milling processes until computational power improves significantly to allow the unconstrained use of DEM.